Question

Consider markov chain with a, b (1-a, a, b, 1-b).

Pₐ,ᵦ = [ 1-a. a ]
[ b 1-b]

for which values of a and b is markov chain irreducible

Answer 1

To ensure the Markov chain is irreducible, both a and b must be non-zero; this guarantees that it is possible to transition from every state to every other state.

Step-by-step explanation:

The student is asking about a Markov chain's irreducibility based on the transition matrix P with transition probabilities that depend on parameters a and b. A Markov chain is irreducible if it is possible to get from every state to every other state in a finite number of steps. This depends on the values of a and b, which should be non-zero for the Markov chain to be irreducible. If a and b are both zero, it means that once you are in a state, you stay in that state forever, and the chain is not irreducible. If a and b are both one, it means that you will switch states every time, which also makes the chain irreducible.